-6h - h² is our answer.
Given,
f(x) = 6x − x2.
f(6 + h) − f(6) h , h ≠ 0
We have to simplify the difference quotient.
We have,
f(x) = 6x − x2
f(6 + h) − f(6)
Find f(6 + h)
f(x) = 6x − x2
f(6+h)
= 6(6+h) - (6+h)^2
Using (a+b)² = a² + 2ab + b²
= 36 + 6h - ( 36 + 12h + h^2 )
= 36 + 6h - 36 - 12h - h^2
= 6h - 12h - h^2
= -6h - h^2
or -(6h + h²)
Find f(6)
f(x) = 6x − x2
f(6)
= 6 x 6 - 6^2
= 36 - 36
= 0
Now,
= f(6 + h) − f(6)
= -6h - h^2 - 0
= -6h - h^2
Thus -6h - h² is our answer.
Learn more about finding difference quotients and simplifying here:
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